LMFDB - Embedded newform 1520.2.bq.q.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1520,2,Mod(31,1520)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1520, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 0, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1520.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1520 = 2^{4} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1520.bq (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.1372611072$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 8x^{10} + 53x^{8} + 86x^{6} + 113x^{4} + 11x^{2} + 1 $ x^12 + 8x^10 + 53x^8 + 86x^6 + 113x^4 + 11*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.2
Root			$0.638510 + 1.10593i$ of defining polynomial
Character	$\chi$	$=$	1520.31
Dual form			1520.2.bq.q.1471.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.391537 - 0.678161i) q^{3} +(-0.500000 - 0.866025i) q^{5} +1.46162i q^{7} +(1.19340 - 2.06703i) q^{9} +O(q^{10})$	\(q+(-0.391537 - 0.678161i) q^{3} +(-0.500000 - 0.866025i) q^{5} +1.46162i q^{7} +(1.19340 - 2.06703i) q^{9} -5.99064i q^{11} +(-3.62524 - 2.09303i) q^{13} +(-0.391537 + 0.678161i) q^{15} +(4.06262 + 7.03666i) q^{17} +(4.31378 - 0.625514i) q^{19} +(0.991212 - 0.572276i) q^{21} +(-3.18133 - 1.83674i) q^{23} +(-0.500000 + 0.866025i) q^{25} -4.21826 q^{27} +(3.55383 + 2.05180i) q^{29} -10.0870 q^{31} +(-4.06262 + 2.34555i) q^{33} +(1.26580 - 0.730808i) q^{35} -7.73262i q^{37} +3.27799i q^{39} +(-0.553830 + 0.319754i) q^{41} +(-6.02015 + 3.47574i) q^{43} -2.38680 q^{45} +(-6.57870 - 3.79821i) q^{47} +4.86368 q^{49} +(3.18133 - 5.51022i) q^{51} +(-4.06262 - 2.34555i) q^{53} +(-5.18804 + 2.99532i) q^{55} +(-2.11320 - 2.68053i) q^{57} +(-1.57737 - 2.73208i) q^{59} +(4.23844 - 7.34119i) q^{61} +(3.02120 + 1.74429i) q^{63} +4.18606i q^{65} +(1.77097 - 3.06740i) q^{67} +2.87660i q^{69} +(-1.33040 - 2.30431i) q^{71} +(1.82418 + 3.15957i) q^{73} +0.783073 q^{75} +8.75602 q^{77} +(-8.31600 - 14.4037i) q^{79} +(-1.92859 - 3.34042i) q^{81} +7.99191i q^{83} +(4.06262 - 7.03666i) q^{85} -3.21343i q^{87} +(-3.00000 - 1.73205i) q^{89} +(3.05921 - 5.29871i) q^{91} +(3.94941 + 6.84059i) q^{93} +(-2.69860 - 3.42309i) q^{95} +(-0.0714065 + 0.0412266i) q^{97} +(-12.3828 - 7.14922i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{5} - 4 q^{9}+O(q^{10}) $ 12 * q - 6 * q^5 - 4 * q^9	$ 12 q - 6 q^{5} - 4 q^{9} + 18 q^{13} + 18 q^{17} + 24 q^{21} - 6 q^{25} + 24 q^{29} - 18 q^{33} + 12 q^{41} + 8 q^{45} - 28 q^{49} - 18 q^{53} - 62 q^{57} + 26 q^{61} + 16 q^{73} + 56 q^{77} - 66 q^{81} + 18 q^{85} - 36 q^{89} - 20 q^{93} + 42 q^{97}+O(q^{100}) $ 12 * q - 6 * q^5 - 4 * q^9 + 18 * q^13 + 18 * q^17 + 24 * q^21 - 6 * q^25 + 24 * q^29 - 18 * q^33 + 12 * q^41 + 8 * q^45 - 28 * q^49 - 18 * q^53 - 62 * q^57 + 26 * q^61 + 16 * q^73 + 56 * q^77 - 66 * q^81 + 18 * q^85 - 36 * q^89 - 20 * q^93 + 42 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times$.

$n$	$191$	$401$	$1141$	$1217$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.391537	−	0.678161i	−0.226054	−	0.391537i	0.730581	−	0.682826i	$-0.239249\pi$
$3$	−0.391537	−	0.678161i	−0.226054	−	0.391537i	−0.956635	+	0.291289i	$0.905916\pi$
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$			1.46162i			0.552439i	0.961095	+	0.276220i	$0.0890817\pi$
$7$			1.46162i			0.552439i	−0.961095	+	0.276220i	$0.910918\pi$
$8$		0			0
$9$	1.19340	−	2.06703i	0.397799	−	0.689009i
$10$		0			0
$11$		−	5.99064i		−	1.80625i	−0.429383	−	0.903123i	$-0.641269\pi$
$11$		−	5.99064i		−	1.80625i	0.429383	−	0.903123i	$-0.358731\pi$
$12$		0			0
$13$	−3.62524	−	2.09303i	−1.00546	−	0.580502i	−0.0956006	−	0.995420i	$-0.530477\pi$
$13$	−3.62524	−	2.09303i	−1.00546	−	0.580502i	−0.909859	+	0.414917i	$0.863810\pi$
$14$		0			0
$15$	−0.391537	+	0.678161i	−0.101094	+	0.175100i
$16$		0			0
$17$	4.06262	+	7.03666i	0.985330	+	1.70664i	0.640462	+	0.767990i	$0.278743\pi$
$17$	4.06262	+	7.03666i	0.985330	+	1.70664i	0.344867	+	0.938651i	$0.387924\pi$
$18$		0			0
$19$	4.31378	−	0.625514i	0.989650	−	0.143503i
$19$	4.31378	−	0.625514i	0.989650	−	0.143503i
$20$		0			0
$21$	0.991212	−	0.572276i	0.216300	−	0.124881i
$22$		0			0
$23$	−3.18133	−	1.83674i	−0.663353	−	0.382987i	0.130201	−	0.991488i	$-0.458438\pi$
$23$	−3.18133	−	1.83674i	−0.663353	−	0.382987i	−0.793553	+	0.608501i	$0.791771\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−4.21826			−0.811804
$28$		0			0
$29$	3.55383	+	2.05180i	0.659930	+	0.381011i	0.792250	−	0.610196i	$-0.208909\pi$
$29$	3.55383	+	2.05180i	0.659930	+	0.381011i	−0.132321	+	0.991207i	$0.542243\pi$
$30$		0			0
$31$	−10.0870			−1.81167			−0.905836	−	0.423629i	$-0.860756\pi$
$31$	−10.0870			−1.81167			−0.905836	+	0.423629i	$0.860756\pi$
$32$		0			0
$33$	−4.06262	+	2.34555i	−0.707211	+	0.408308i
$34$		0			0
$35$	1.26580	−	0.730808i	0.213959	−	0.123529i
$36$		0			0
$37$		−	7.73262i		−	1.27123i	−0.772004	−	0.635617i	$-0.780746\pi$
$37$		−	7.73262i		−	1.27123i	0.772004	−	0.635617i	$-0.219254\pi$
$38$		0			0
$39$			3.27799i			0.524899i
$40$		0			0
$41$	−0.553830	+	0.319754i	−0.0864937	+	0.0499372i	−0.542623	−	0.839976i	$-0.682569\pi$
$41$	−0.553830	+	0.319754i	−0.0864937	+	0.0499372i	0.456129	+	0.889914i	$0.349235\pi$
$42$		0			0
$43$	−6.02015	+	3.47574i	−0.918065	+	0.530045i	−0.883017	−	0.469341i	$-0.844492\pi$
$43$	−6.02015	+	3.47574i	−0.918065	+	0.530045i	−0.0350475	+	0.999386i	$0.511158\pi$
$44$		0			0
$45$	−2.38680			−0.355803
$46$		0			0
$47$	−6.57870	−	3.79821i	−0.959602	−	0.554026i	−0.0635512	−	0.997979i	$-0.520243\pi$
$47$	−6.57870	−	3.79821i	−0.959602	−	0.554026i	−0.896050	+	0.443952i	$0.853576\pi$
$48$		0			0
$49$	4.86368			0.694811
$50$		0			0
$51$	3.18133	−	5.51022i	0.445475	−	0.771585i
$52$		0			0
$53$	−4.06262	−	2.34555i	−0.558044	−	0.322187i	0.194316	−	0.980939i	$-0.437751\pi$
$53$	−4.06262	−	2.34555i	−0.558044	−	0.322187i	−0.752360	+	0.658752i	$0.771085\pi$
$54$		0			0
$55$	−5.18804	+	2.99532i	−0.699556	+	0.403889i
$56$		0			0
$57$	−2.11320	−	2.68053i	−0.279901	−	0.355045i
$58$		0			0
$59$	−1.57737	−	2.73208i	−0.205356	−	0.355687i	0.744890	−	0.667187i	$-0.232502\pi$
$59$	−1.57737	−	2.73208i	−0.205356	−	0.355687i	−0.950246	+	0.311500i	$0.899169\pi$
$60$		0			0
$61$	4.23844	−	7.34119i	0.542677	−	0.939944i	−0.456073	−	0.889943i	$-0.650744\pi$
$61$	4.23844	−	7.34119i	0.542677	−	0.939944i	0.998749	−	0.0500009i	$-0.0159224\pi$
$62$		0			0
$63$	3.02120	+	1.74429i	0.380635	+	0.219760i
$64$		0			0
$65$			4.18606i			0.519217i
$66$		0			0
$67$	1.77097	−	3.06740i	0.216358	−	0.374743i	−0.737334	−	0.675529i	$-0.763915\pi$
$67$	1.77097	−	3.06740i	0.216358	−	0.374743i	0.953692	+	0.300785i	$0.0972488\pi$
$68$		0			0
$69$			2.87660i			0.346302i
$70$		0			0
$71$	−1.33040	−	2.30431i	−0.157889	−	0.273472i	0.776218	−	0.630464i	$-0.217135\pi$
$71$	−1.33040	−	2.30431i	−0.157889	−	0.273472i	−0.934107	+	0.356993i	$0.883802\pi$
$72$		0			0
$73$	1.82418	+	3.15957i	0.213504	+	0.369800i	0.952809	−	0.303571i	$-0.0981791\pi$
$73$	1.82418	+	3.15957i	0.213504	+	0.369800i	−0.739305	+	0.673371i	$0.764846\pi$
$74$		0			0
$75$	0.783073			0.0904215
$76$		0			0
$77$	8.75602			0.997841
$78$		0			0
$79$	−8.31600	−	14.4037i	−0.935623	−	1.62055i	−0.773520	−	0.633772i	$-0.781506\pi$
$79$	−8.31600	−	14.4037i	−0.935623	−	1.62055i	−0.162103	−	0.986774i	$-0.551828\pi$
$80$		0			0
$81$	−1.92859	−	3.34042i	−0.214288	−	0.371158i
$82$		0			0
$83$			7.99191i			0.877226i	0.898676	+	0.438613i	$0.144530\pi$
$83$			7.99191i			0.877226i	−0.898676	+	0.438613i	$0.855470\pi$
$84$		0			0
$85$	4.06262	−	7.03666i	0.440653	−	0.763233i
$86$		0			0
$87$		−	3.21343i		−	0.344515i
$88$		0			0
$89$	−3.00000	−	1.73205i	−0.317999	−	0.183597i	0.332501	−	0.943103i	$-0.392107\pi$
$89$	−3.00000	−	1.73205i	−0.317999	−	0.183597i	−0.650500	+	0.759506i	$0.725441\pi$
$90$		0			0
$91$	3.05921	−	5.29871i	0.320692	−	0.555455i
$92$		0			0
$93$	3.94941	+	6.84059i	0.409535	+	0.709336i
$94$		0			0
$95$	−2.69860	−	3.42309i	−0.276871	−	0.351202i
$96$		0			0
$97$	−0.0714065	+	0.0412266i	−0.00725023	+	0.00418592i	−0.503621	−	0.863925i	$-0.667999\pi$
$97$	−0.0714065	+	0.0412266i	−0.00725023	+	0.00418592i	0.496371	+	0.868111i	$0.334666\pi$
$98$		0			0
$99$	−12.3828	−	7.14922i	−1.24452	−	0.718523i
$100$		0			0
$101$	−6.81863	+	11.8102i	−0.678480	+	1.17516i	0.296959	+	0.954890i	$0.404027\pi$
$101$	−6.81863	+	11.8102i	−0.678480	+	1.17516i	−0.975439	+	0.220271i	$0.929306\pi$
$102$		0			0
$103$	9.28144			0.914528			0.457264	−	0.889331i	$-0.348829\pi$
$103$	9.28144			0.914528			0.457264	+	0.889331i	$0.348829\pi$
$104$		0			0
$105$	−0.991212	−	0.572276i	−0.0967324	−	0.0558485i
$106$		0			0
$107$	−12.4137			−1.20008			−0.600041	−	0.799970i	$-0.704849\pi$
$107$	−12.4137			−1.20008			−0.600041	+	0.799970i	$0.704849\pi$
$108$		0			0
$109$	−9.74168	+	5.62436i	−0.933084	+	0.538716i	−0.887786	−	0.460257i	$-0.847757\pi$
$109$	−9.74168	+	5.62436i	−0.933084	+	0.538716i	−0.0452985	+	0.998973i	$0.514424\pi$
$110$		0			0
$111$	−5.24396	+	3.02760i	−0.497735	+	0.287367i
$112$		0			0
$113$		−	10.6397i		−	1.00090i	−0.865767	−	0.500448i	$-0.833169\pi$
$113$		−	10.6397i		−	1.00090i	0.865767	−	0.500448i	$-0.166831\pi$
$114$		0			0
$115$			3.67348i			0.342554i
$116$		0			0
$117$	−8.65270	+	4.99564i	−0.799943	+	0.461847i
$118$		0			0
$119$	−10.2849	+	5.93799i	−0.942815	+	0.544335i
$120$		0			0
$121$	−24.8877			−2.26252
$122$		0			0
$123$	0.433689	+	0.250391i	0.0391045	+	0.0225770i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	8.80994	−	15.2593i	0.781756	−	1.35404i	−0.149162	−	0.988813i	$-0.547658\pi$
$127$	8.80994	−	15.2593i	0.781756	−	1.35404i	0.930918	−	0.365228i	$-0.119009\pi$
$128$		0			0
$129$	4.71422	+	2.72176i	0.415064	+	0.239637i
$130$		0			0
$131$	6.57870	−	3.79821i	0.574783	−	0.331851i	−0.184274	−	0.982875i	$-0.558993\pi$
$131$	6.57870	−	3.79821i	0.574783	−	0.331851i	0.759058	+	0.651023i	$0.225660\pi$
$132$		0			0
$133$	0.914262	+	6.30510i	0.0792766	+	0.546721i
$134$		0			0
$135$	2.10913	+	3.65312i	0.181525	+	0.314410i
$136$		0			0
$137$	−6.50879	+	11.2736i	−0.556083	+	0.963165i	0.441735	+	0.897146i	$0.354363\pi$
$137$	−6.50879	+	11.2736i	−0.556083	+	0.963165i	−0.997818	+	0.0660190i	$0.978970\pi$
$138$		0			0
$139$	−5.58646	−	3.22535i	−0.473838	−	0.273570i	0.244007	−	0.969773i	$-0.421538\pi$
$139$	−5.58646	−	3.22535i	−0.473838	−	0.273570i	−0.717845	+	0.696203i	$0.754871\pi$
$140$		0			0
$141$			5.94856i			0.500959i
$142$		0			0
$143$	−12.5386	+	21.7175i	−1.04853	+	1.81611i
$144$		0			0
$145$		−	4.10361i		−	0.340786i
$146$		0			0
$147$	−1.90431	−	3.29836i	−0.157065	−	0.272044i
$148$		0			0
$149$	0.193398	+	0.334976i	0.0158438	+	0.0274423i	0.873839	−	0.486216i	$-0.161623\pi$
$149$	0.193398	+	0.334976i	0.0158438	+	0.0274423i	−0.857995	+	0.513658i	$0.828290\pi$
$150$		0			0
$151$	6.44696			0.524646			0.262323	−	0.964980i	$-0.415511\pi$
$151$	6.44696			0.524646			0.262323	+	0.964980i	$0.415511\pi$
$152$		0			0
$153$	19.3933			1.56785
$154$		0			0
$155$	5.04348	+	8.73557i	0.405102	+	0.701658i
$156$		0			0
$157$	−0.621992	−	1.07732i	−0.0496403	−	0.0859796i	0.840138	−	0.542373i	$-0.182474\pi$
$157$	−0.621992	−	1.07732i	−0.0496403	−	0.0859796i	−0.889778	+	0.456394i	$0.849141\pi$
$158$		0			0
$159$			3.67348i			0.291326i
$160$		0			0
$161$	2.68461	−	4.64988i	0.211577	−	0.366462i
$162$		0			0
$163$			5.27927i			0.413504i	0.978393	+	0.206752i	$0.0662894\pi$
$163$			5.27927i			0.413504i	−0.978393	+	0.206752i	$0.933711\pi$
$164$		0			0
$165$	4.06262	+	2.34555i	0.316274	+	0.182601i
$166$		0			0
$167$	−6.26713	+	10.8550i	−0.484965	+	0.839984i	−0.999851	−	0.0172750i	$-0.994501\pi$
$167$	−6.26713	+	10.8550i	−0.484965	+	0.839984i	0.514886	+	0.857259i	$0.327834\pi$
$168$		0			0
$169$	2.26156	+	3.91714i	0.173966	+	0.301318i
$170$		0			0
$171$	3.85511	−	9.66319i	0.294807	−	0.738963i
$172$		0			0
$173$	7.42859	−	4.28890i	0.564786	−	0.326079i	−0.190278	−	0.981730i	$-0.560939\pi$
$173$	7.42859	−	4.28890i	0.564786	−	0.326079i	0.755064	+	0.655651i	$0.227606\pi$
$174$		0			0
$175$	−1.26580	−	0.730808i	−0.0956853	−	0.0552439i
$176$		0			0
$177$	−1.23520	+	2.13942i	−0.0928430	+	0.160809i
$178$		0			0
$179$	25.1390			1.87898			0.939490	−	0.342576i	$-0.111299\pi$
$179$	25.1390			1.87898			0.939490	+	0.342576i	$0.111299\pi$
$180$		0			0
$181$	−9.53515	−	5.50512i	−0.708742	−	0.409193i	0.101853	−	0.994799i	$-0.467523\pi$
$181$	−9.53515	−	5.50512i	−0.708742	−	0.409193i	−0.810595	+	0.585607i	$0.800856\pi$
$182$		0			0
$183$	−6.63802			−0.490696
$184$		0			0
$185$	−6.69664	+	3.86631i	−0.492347	+	0.284257i
$186$		0			0
$187$	42.1541	−	24.3377i	3.08261	−	1.77975i
$188$		0			0
$189$		−	6.16547i		−	0.448472i
$190$		0			0
$191$		−	1.71108i		−	0.123810i	−0.998082	−	0.0619048i	$-0.980282\pi$
$191$		−	1.71108i		−	0.123810i	0.998082	−	0.0619048i	$-0.0197175\pi$
$192$		0			0
$193$	10.2955	−	5.94412i	0.741087	−	0.427867i	−0.0813772	−	0.996683i	$-0.525932\pi$
$193$	10.2955	−	5.94412i	0.741087	−	0.427867i	0.822465	+	0.568816i	$0.192598\pi$
$194$		0			0
$195$	2.83883	−	1.63900i	0.203293	−	0.117371i
$196$		0			0
$197$	22.0966			1.57432			0.787158	−	0.616752i	$-0.211552\pi$
$197$	22.0966			1.57432			0.787158	+	0.616752i	$0.211552\pi$
$198$		0			0
$199$	13.2502	+	7.65000i	0.939281	+	0.542294i	0.889735	−	0.456478i	$-0.150889\pi$
$199$	13.2502	+	7.65000i	0.939281	+	0.542294i	0.0495460	+	0.998772i	$0.484223\pi$
$200$		0			0
$201$	−2.77359			−0.195634
$202$		0			0
$203$	−2.99895	+	5.19434i	−0.210485	+	0.364571i
$204$		0			0
$205$	0.553830	+	0.319754i	0.0386812	+	0.0223326i
$206$		0			0
$207$	−7.59318	+	4.38392i	−0.527763	+	0.304704i
$208$		0			0
$209$	−3.74723	−	25.8423i	−0.259201	−	1.78755i
$210$		0			0
$211$	−8.60512	−	14.9045i	−0.592401	−	1.02607i	−0.993908	−	0.110213i	$-0.964847\pi$
$211$	−8.60512	−	14.9045i	−0.592401	−	1.02607i	0.401507	−	0.915856i	$-0.368487\pi$
$212$		0			0
$213$	−1.04180	+	1.80445i	−0.0713828	+	0.123639i
$214$		0			0
$215$	6.02015	+	3.47574i	0.410571	+	0.237043i
$216$		0			0
$217$		−	14.7433i		−	1.00084i
$218$		0			0
$219$	1.42846	−	2.47417i	0.0965267	−	0.167189i
$220$		0			0
$221$		−	34.0127i		−	2.28795i
$222$		0			0
$223$	8.23603	+	14.2652i	0.551525	+	0.955270i	0.998165	+	0.0605560i	$0.0192874\pi$
$223$	8.23603	+	14.2652i	0.551525	+	0.955270i	−0.446639	+	0.894714i	$0.647379\pi$
$224$		0			0
$225$	1.19340	+	2.06703i	0.0795599	+	0.137802i
$226$		0			0
$227$	4.93947			0.327844			0.163922	−	0.986473i	$-0.447585\pi$
$227$	4.93947			0.327844			0.163922	+	0.986473i	$0.447585\pi$
$228$		0			0
$229$	3.11875			0.206093			0.103046	−	0.994677i	$-0.467141\pi$
$229$	3.11875			0.206093			0.103046	+	0.994677i	$0.467141\pi$
$230$		0			0
$231$	−3.42830	−	5.93799i	−0.225566	−	0.390691i
$232$		0			0
$233$	2.72965	+	4.72790i	0.178825	+	0.309735i	0.941479	−	0.337073i	$-0.109437\pi$
$233$	2.72965	+	4.72790i	0.178825	+	0.309735i	−0.762653	+	0.646808i	$0.776104\pi$
$234$		0			0
$235$			7.59643i			0.495536i
$236$		0			0
$237$	−6.51203	+	11.2792i	−0.423002	+	0.732661i
$238$		0			0
$239$			9.91358i			0.641256i	0.947205	+	0.320628i	$0.103894\pi$
$239$			9.91358i			0.641256i	−0.947205	+	0.320628i	$0.896106\pi$
$240$		0			0
$241$	22.2505	+	12.8463i	1.43328	+	0.827504i	0.997369	−	0.0724865i	$-0.0230934\pi$
$241$	22.2505	+	12.8463i	1.43328	+	0.827504i	0.435910	+	0.899990i	$0.356427\pi$
$242$		0			0
$243$	−7.83761	+	13.5751i	−0.502783	+	0.870846i
$244$		0			0
$245$	−2.43184	−	4.21207i	−0.155364	−	0.269099i
$246$		0			0
$247$	−16.9477	−	6.76125i	−1.07836	−	0.430208i
$248$		0			0
$249$	5.41981	−	3.12913i	0.343466	−	0.198300i
$250$		0			0
$251$	−13.5797	−	7.84022i	−0.857141	−	0.494870i	0.00591296	−	0.999983i	$-0.498118\pi$
$251$	−13.5797	−	7.84022i	−0.857141	−	0.494870i	−0.863054	+	0.505112i	$0.831451\pi$
$252$		0			0
$253$	−11.0032	+	19.0582i	−0.691768	+	1.19818i
$254$		0			0
$255$	−6.36265			−0.398445
$256$		0			0
$257$	−12.2142	−	7.05188i	−0.761902	−	0.439884i	0.0680762	−	0.997680i	$-0.478314\pi$
$257$	−12.2142	−	7.05188i	−0.761902	−	0.439884i	−0.829978	+	0.557796i	$0.811647\pi$
$258$		0			0
$259$	11.3021			0.702280
$260$		0			0
$261$	8.48227	−	4.89724i	0.525039	−	0.303132i
$262$		0			0
$263$	−15.5066	+	8.95275i	−0.956179	+	0.552050i	−0.894995	−	0.446076i	$-0.852821\pi$
$263$	−15.5066	+	8.95275i	−0.956179	+	0.552050i	−0.0611839	+	0.998127i	$0.519488\pi$
$264$		0			0
$265$			4.69111i			0.288172i
$266$		0			0
$267$			2.71264i			0.166011i
$268$		0			0
$269$	−5.75047	+	3.32004i	−0.350613	+	0.202426i	−0.664955	−	0.746883i	$-0.731549\pi$
$269$	−5.75047	+	3.32004i	−0.350613	+	0.202426i	0.314342	+	0.949310i	$0.398216\pi$
$270$		0			0
$271$	11.6403	−	6.72052i	0.707097	−	0.408243i	−0.102888	−	0.994693i	$-0.532808\pi$
$271$	11.6403	−	6.72052i	0.707097	−	0.408243i	0.809985	+	0.586450i	$0.199475\pi$
$272$		0			0
$273$	−4.79117			−0.289975
$274$		0			0
$275$	5.18804	+	2.99532i	0.312851	+	0.180625i
$276$		0			0
$277$	14.7736			0.887659			0.443830	−	0.896111i	$-0.353620\pi$
$277$	14.7736			0.887659			0.443830	+	0.896111i	$0.353620\pi$
$278$		0			0
$279$	−12.0378	+	20.8500i	−0.720682	+	1.24826i
$280$		0			0
$281$	12.1692	+	7.02588i	0.725952	+	0.419129i	0.816940	−	0.576723i	$-0.195669\pi$
$281$	12.1692	+	7.02588i	0.725952	+	0.419129i	−0.0909873	+	0.995852i	$0.529002\pi$
$282$		0			0
$283$	10.9922	−	6.34632i	0.653416	−	0.377250i	−0.136348	−	0.990661i	$-0.543537\pi$
$283$	10.9922	−	6.34632i	0.653416	−	0.377250i	0.789764	+	0.613411i	$0.210203\pi$
$284$		0			0
$285$	−1.26480	+	3.17035i	−0.0749206	+	0.187795i
$286$		0			0
$287$	−0.467358	−	0.809487i	−0.0275873	−	0.0477825i
$288$		0			0
$289$	−24.5097	+	42.4521i	−1.44175	+	2.49718i
$290$		0			0
$291$	0.0559165	+	0.0322834i	0.00327788	+	0.00189249i
$292$		0			0
$293$		−	15.8054i		−	0.923360i	−0.887047	−	0.461680i	$-0.847247\pi$
$293$		−	15.8054i		−	0.923360i	0.887047	−	0.461680i	$-0.152753\pi$
$294$		0			0
$295$	−1.57737	+	2.73208i	−0.0918380	+	0.159068i
$296$		0			0
$297$			25.2700i			1.46632i
$298$		0			0
$299$	7.68871	+	13.3172i	0.444650	+	0.770156i
$300$		0			0
$301$	−5.08019	−	8.79916i	−0.292818	−	0.507175i
$302$		0			0
$303$	10.6790			0.613491
$304$		0			0
$305$	−8.47688			−0.485385
$306$		0			0
$307$	13.4284	+	23.2587i	0.766400	+	1.32744i	0.939503	+	0.342540i	$0.111287\pi$
$307$	13.4284	+	23.2587i	0.766400	+	1.32744i	−0.173103	+	0.984904i	$0.555379\pi$
$308$		0			0
$309$	−3.63402	−	6.29432i	−0.206732	−	0.358071i
$310$		0			0
$311$		−	23.9237i		−	1.35659i	−0.734791	−	0.678294i	$-0.762720\pi$
$311$		−	23.9237i		−	1.35659i	0.734791	−	0.678294i	$-0.237280\pi$
$312$		0			0
$313$	2.84175	−	4.92206i	0.160625	−	0.278211i	−0.774468	−	0.632613i	$-0.781982\pi$
$313$	2.84175	−	4.92206i	0.160625	−	0.278211i	0.935093	+	0.354402i	$0.115316\pi$
$314$		0			0
$315$		−	3.48858i		−	0.196559i
$316$		0			0
$317$	−19.8493	−	11.4600i	−1.11485	−	0.643659i	−0.174769	−	0.984609i	$-0.555918\pi$
$317$	−19.8493	−	11.4600i	−1.11485	−	0.643659i	−0.940081	+	0.340950i	$0.889251\pi$
$318$		0			0
$319$	12.2916	−	21.2897i	0.688199	−	1.19199i
$320$		0			0
$321$	4.86043	+	8.41851i	0.271283	+	0.469876i
$322$		0			0
$323$	21.9268	+	27.8134i	1.22004	+	1.54758i
$324$		0			0
$325$	3.62524	−	2.09303i	0.201092	−	0.116100i
$326$		0			0
$327$	7.62845	+	4.40429i	0.421854	+	0.243558i
$328$		0			0
$329$	5.55153	−	9.61553i	0.306066	−	0.530122i
$330$		0			0
$331$	18.6165			1.02325			0.511627	−	0.859208i	$-0.329043\pi$
$331$	18.6165			1.02325			0.511627	+	0.859208i	$0.329043\pi$
$332$		0			0
$333$	−15.9835	−	9.22809i	−0.875892	−	0.505696i
$334$		0			0
$335$	−3.54193			−0.193517
$336$		0			0
$337$	30.3757	−	17.5374i	1.65467	−	0.955324i	0.679555	−	0.733624i	$-0.262173\pi$
$337$	30.3757	−	17.5374i	1.65467	−	0.955324i	0.975115	−	0.221700i	$-0.0711606\pi$
$338$		0			0
$339$	−7.21541	+	4.16582i	−0.391887	+	0.226256i
$340$		0			0
$341$			60.4273i			3.27232i
$342$		0			0
$343$			17.3401i			0.936280i
$344$		0			0
$345$	2.49121	−	1.43830i	0.134122	−	0.0774356i
$346$		0			0
$347$	23.6263	−	13.6406i	1.26832	−	0.732268i	0.293654	−	0.955912i	$-0.405129\pi$
$347$	23.6263	−	13.6406i	1.26832	−	0.732268i	0.974671	+	0.223644i	$0.0717953\pi$
$348$		0			0
$349$	23.0416			1.23339			0.616695	−	0.787202i	$-0.288471\pi$
$349$	23.0416			1.23339			0.616695	+	0.787202i	$0.288471\pi$
$350$		0			0
$351$	15.2922	+	8.82894i	0.816236	+	0.471254i
$352$		0			0
$353$	−23.3998			−1.24544			−0.622722	−	0.782443i	$-0.713973\pi$
$353$	−23.3998			−1.24544			−0.622722	+	0.782443i	$0.713973\pi$
$354$		0			0
$355$	−1.33040	+	2.30431i	−0.0706101	+	0.122300i
$356$		0			0
$357$	8.05383	+	4.64988i	0.426254	+	0.246098i
$358$		0			0
$359$	4.75436	−	2.74493i	0.250925	−	0.144872i	−0.369263	−	0.929325i	$-0.620390\pi$
$359$	4.75436	−	2.74493i	0.250925	−	0.144872i	0.620188	+	0.784453i	$0.287056\pi$
$360$		0			0
$361$	18.2175	−	5.39667i	0.958814	−	0.284035i
$362$		0			0
$363$	9.74446	+	16.8779i	0.511452	+	0.885860i
$364$		0			0
$365$	1.82418	−	3.15957i	0.0954819	−	0.165379i
$366$		0			0
$367$	5.15438	+	2.97588i	0.269056	+	0.155340i	0.628459	−	0.777843i	$-0.283686\pi$
$367$	5.15438	+	2.97588i	0.269056	+	0.155340i	−0.359402	+	0.933183i	$0.617019\pi$
$368$		0			0
$369$			1.52638i			0.0794599i
$370$		0			0
$371$	3.42830	−	5.93799i	0.177988	−	0.308285i
$372$		0			0
$373$			3.04151i			0.157483i	0.996895	+	0.0787417i	$0.0250902\pi$
$373$			3.04151i			0.157483i	−0.996895	+	0.0787417i	$0.974910\pi$
$374$		0			0
$375$	−0.391537	−	0.678161i	−0.0202189	−	0.0350201i
$376$		0			0
$377$	−8.58898	−	14.8766i	−0.442355	−	0.766182i
$378$		0			0
$379$	−5.53469			−0.284298			−0.142149	−	0.989845i	$-0.545401\pi$
$379$	−5.53469			−0.284298			−0.142149	+	0.989845i	$0.545401\pi$
$380$		0			0
$381$	−13.7977			−0.706875
$382$		0			0
$383$	6.14935	+	10.6510i	0.314217	+	0.544240i	0.979271	−	0.202556i	$-0.0649247\pi$
$383$	6.14935	+	10.6510i	0.314217	+	0.544240i	−0.665054	+	0.746796i	$0.731591\pi$
$384$		0			0
$385$	−4.37801	−	7.58293i	−0.223124	−	0.386462i
$386$		0			0
$387$			16.5918i			0.843406i
$388$		0			0
$389$	−1.33297	+	2.30877i	−0.0675841	+	0.117059i	−0.897837	−	0.440327i	$-0.854862\pi$
$389$	−1.33297	+	2.30877i	−0.0675841	+	0.117059i	0.830253	+	0.557386i	$0.188196\pi$
$390$		0			0
$391$		−	29.8479i		−	1.50947i
$392$		0			0
$393$	−5.15160	−	2.97428i	−0.259864	−	0.150032i
$394$		0			0
$395$	−8.31600	+	14.4037i	−0.418423	+	0.724730i
$396$		0			0
$397$	−7.55383	−	13.0836i	−0.379116	−	0.656648i	0.611818	−	0.790999i	$-0.290438\pi$
$397$	−7.55383	−	13.0836i	−0.379116	−	0.656648i	−0.990934	+	0.134351i	$0.957105\pi$
$398$		0			0
$399$	3.91791	−	3.08869i	0.196141	−	0.154628i
$400$		0			0
$401$	10.3836	−	5.99495i	0.518530	−	0.299373i	−0.217803	−	0.975993i	$-0.569889\pi$
$401$	10.3836	−	5.99495i	0.518530	−	0.299373i	0.736333	+	0.676619i	$0.236556\pi$
$402$		0			0
$403$	36.5676	+	21.1123i	1.82156	+	1.05168i
$404$		0			0
$405$	−1.92859	+	3.34042i	−0.0958326	+	0.165987i
$406$		0			0
$407$	−46.3233			−2.29616
$408$		0			0
$409$	−22.5450	−	13.0164i	−1.11478	−	0.643619i	−0.174717	−	0.984619i	$-0.555901\pi$
$409$	−22.5450	−	13.0164i	−1.11478	−	0.643619i	−0.940063	+	0.341000i	$0.889234\pi$
$410$		0			0
$411$	10.1937			0.502819
$412$		0			0
$413$	3.99326	−	2.30551i	0.196495	−	0.113447i
$414$		0			0
$415$	6.92120	−	3.99596i	0.339748	−	0.196154i
$416$		0			0
$417$			5.05136i			0.247366i
$418$		0			0
$419$		−	30.6646i		−	1.49806i	−0.662535	−	0.749031i	$-0.730519\pi$
$419$		−	30.6646i		−	1.49806i	0.662535	−	0.749031i	$-0.269481\pi$
$420$		0			0
$421$	26.7152	−	15.4240i	1.30202	−	0.751720i	0.321268	−	0.946988i	$-0.395891\pi$
$421$	26.7152	−	15.4240i	1.30202	−	0.751720i	0.980750	+	0.195268i	$0.0625578\pi$
$422$		0			0
$423$	−15.7020	+	9.06556i	−0.763458	+	0.440783i
$424$		0			0
$425$	−8.12524			−0.394132
$426$		0			0
$427$	10.7300	+	6.19497i	0.519262	+	0.299796i
$428$		0			0
$429$	19.6373			0.948096
$430$		0			0
$431$	−8.30477	+	14.3843i	−0.400027	+	0.692867i	−0.993729	−	0.111818i	$-0.964333\pi$
$431$	−8.30477	+	14.3843i	−0.400027	+	0.692867i	0.593702	+	0.804685i	$0.297666\pi$
$432$		0			0
$433$	−25.8404	−	14.9190i	−1.24181	−	0.716960i	−0.272348	−	0.962199i	$-0.587800\pi$
$433$	−25.8404	−	14.9190i	−1.24181	−	0.716960i	−0.969463	+	0.245239i	$0.921133\pi$
$434$		0			0
$435$	−2.78291	+	1.60671i	−0.133430	+	0.0770360i
$436$		0			0
$437$	−14.8725	−	5.93334i	−0.711446	−	0.283830i
$438$		0			0
$439$	1.19706	+	2.07336i	0.0571323	+	0.0989561i	0.893177	−	0.449705i	$-0.148471\pi$
$439$	1.19706	+	2.07336i	0.0571323	+	0.0989561i	−0.836045	+	0.548661i	$0.815138\pi$
$440$		0			0
$441$	5.80430	−	10.0533i	0.276395	−	0.478731i
$442$		0			0
$443$	−23.9351	−	13.8189i	−1.13719	−	0.656558i	−0.191458	−	0.981501i	$-0.561321\pi$
$443$	−23.9351	−	13.8189i	−1.13719	−	0.656558i	−0.945734	+	0.324943i	$0.894655\pi$
$444$		0			0
$445$			3.46410i			0.164214i
$446$		0			0
$447$	0.151445	−	0.262310i	0.00716310	−	0.0124069i
$448$		0			0
$449$		−	5.98933i		−	0.282654i	−0.989963	−	0.141327i	$-0.954863\pi$
$449$		−	5.98933i		−	0.282654i	0.989963	−	0.141327i	$-0.0451369\pi$
$450$		0			0
$451$	1.91553	+	3.31780i	0.0901988	+	0.156229i
$452$		0			0
$453$	−2.52422	−	4.37208i	−0.118598	−	0.205418i
$454$		0			0
$455$	−6.11842			−0.286836
$456$		0			0
$457$	24.1252			1.12853			0.564265	−	0.825593i	$-0.309159\pi$
$457$	24.1252			1.12853			0.564265	+	0.825593i	$0.309159\pi$
$458$		0			0
$459$	−17.1372	−	29.6824i	−0.799894	−	1.38546i
$460$		0			0
$461$	−8.04829	−	13.9400i	−0.374846	−	0.649252i	0.615458	−	0.788170i	$-0.288971\pi$
$461$	−8.04829	−	13.9400i	−0.374846	−	0.649252i	−0.990304	+	0.138917i	$0.955638\pi$
$462$		0			0
$463$			9.30936i			0.432643i	0.976322	+	0.216321i	$0.0694059\pi$
$463$			9.30936i			0.432643i	−0.976322	+	0.216321i	$0.930594\pi$
$464$		0			0
$465$	3.94941	−	6.84059i	0.183150	−	0.317225i
$466$		0			0
$467$		−	4.31843i		−	0.199833i	−0.994996	−	0.0999166i	$-0.968142\pi$
$467$		−	4.31843i		−	0.199833i	0.994996	−	0.0999166i	$-0.0318576\pi$
$468$		0			0
$469$	4.48337	+	2.58847i	0.207023	+	0.119525i
$470$		0			0
$471$	−0.487065	+	0.843621i	−0.0224428	+	0.0388720i
$472$		0			0
$473$	20.8219	+	36.0646i	0.957391	+	1.65825i
$474$		0			0
$475$	−1.61518	+	4.04860i	−0.0741096	+	0.185763i
$476$		0			0
$477$	−9.69664	+	5.59836i	−0.443979	+	0.256331i
$478$		0			0
$479$	36.5546	+	21.1048i	1.67022	+	0.964303i	0.967511	+	0.252828i	$0.0813608\pi$
$479$	36.5546	+	21.1048i	1.67022	+	0.964303i	0.702711	+	0.711475i	$0.251973\pi$
$480$		0			0
$481$	−16.1846	+	28.0326i	−0.737955	+	1.27818i
$482$		0			0
$483$	−4.20449			−0.191311
$484$		0			0
$485$	0.0714065	+	0.0412266i	0.00324240	+	0.00187200i
$486$		0			0
$487$	18.6921			0.847019			0.423510	−	0.905892i	$-0.360798\pi$
$487$	18.6921			0.847019			0.423510	+	0.905892i	$0.360798\pi$
$488$		0			0
$489$	3.58019	−	2.06703i	0.161902	−	0.0934742i
$490$		0			0
$491$	7.26210	−	4.19277i	0.327734	−	0.189217i	−0.327101	−	0.944990i	$-0.606072\pi$
$491$	7.26210	−	4.19277i	0.327734	−	0.189217i	0.654835	+	0.755772i	$0.272738\pi$
$492$		0			0
$493$			33.3428i			1.50168i
$494$		0			0
$495$			14.2984i			0.642667i
$496$		0			0
$497$	3.36802	−	1.94453i	0.151076	−	0.0872240i
$498$		0			0
$499$	−16.5786	+	9.57167i	−0.742161	+	0.428487i	−0.822854	−	0.568252i	$-0.807620\pi$
$499$	−16.5786	+	9.57167i	−0.742161	+	0.428487i	0.0806936	+	0.996739i	$0.474286\pi$
$500$		0			0
$501$	9.81524			0.438512
$502$		0			0
$503$	25.9402	+	14.9766i	1.15662	+	0.667773i	0.950491	−	0.310752i	$-0.100581\pi$
$503$	25.9402	+	14.9766i	1.15662	+	0.667773i	0.206126	+	0.978525i	$0.433914\pi$
$504$		0			0
$505$	13.6373			0.606851
$506$		0			0
$507$	1.77097	−	3.06740i	0.0786514	−	0.136228i
$508$		0			0
$509$	8.40317	+	4.85158i	0.372464	+	0.215042i	0.674534	−	0.738243i	$-0.264344\pi$
$509$	8.40317	+	4.85158i	0.372464	+	0.215042i	−0.302070	+	0.953286i	$0.597678\pi$
$510$		0			0
$511$	−4.61808	+	2.66625i	−0.204292	+	0.117948i
$512$		0			0
$513$	−18.1966	+	2.63858i	−0.803401	+	0.116496i
$514$		0			0
$515$	−4.64072	−	8.03797i	−0.204495	−	0.354195i
$516$		0			0
$517$	−22.7537	+	39.4106i	−1.00071	+	1.73328i
$518$		0			0
$519$	−5.81713	−	3.35852i	−0.255344	−	0.147423i
$520$		0			0
$521$		−	15.2268i		−	0.667096i	−0.942733	−	0.333548i	$-0.891754\pi$
$521$		−	15.2268i		−	0.667096i	0.942733	−	0.333548i	$-0.108246\pi$
$522$		0			0
$523$	14.4919	−	25.1008i	0.633688	−	1.09758i	−0.353103	−	0.935584i	$-0.614874\pi$
$523$	14.4919	−	25.1008i	0.633688	−	1.09758i	0.986791	−	0.161996i	$-0.0517930\pi$
$524$		0			0
$525$			1.14455i			0.0499524i
$526$		0			0
$527$	−40.9795	−	70.9785i	−1.78509	−	3.09187i
$528$		0			0
$529$	−4.75277	−	8.23204i	−0.206642	−	0.357915i
$530$		0			0
$531$	−7.52972			−0.326762
$532$		0			0
$533$	2.67702			0.115955
$534$		0			0
$535$	6.20687	+	10.7506i	0.268346	+	0.464789i
$536$		0			0
$537$	−9.84286	−	17.0483i	−0.424751	−	0.735690i
$538$		0			0
$539$		−	29.1365i		−	1.25500i
$540$		0			0
$541$	−5.65160	+	9.78886i	−0.242981	+	0.420856i	−0.961562	−	0.274587i	$-0.911459\pi$
$541$	−5.65160	+	9.78886i	−0.242981	+	0.420856i	0.718581	+	0.695443i	$0.244792\pi$
$542$		0			0
$543$			8.62183i			0.369998i
$544$		0			0
$545$	9.74168	+	5.62436i	0.417288	+	0.240921i
$546$		0			0
$547$	0.140222	−	0.242872i	0.00599547	−	0.0103845i	−0.863012	−	0.505183i	$-0.831425\pi$
$547$	0.140222	−	0.242872i	0.00599547	−	0.0103845i	0.869008	+	0.494799i	$0.164758\pi$
$548$		0			0
$549$	−10.1163	−	17.5219i	−0.431753	−	0.747818i
$550$		0			0
$551$	16.6139	+	6.62807i	0.707775	+	0.282365i
$552$		0			0
$553$	21.0527	−	12.1548i	0.895253	−	0.516875i
$554$		0			0
$555$	5.24396	+	3.02760i	0.222594	+	0.128515i
$556$		0			0
$557$	−11.6340	+	20.1507i	−0.492949	+	0.853813i	−0.999967	−	0.00812223i	$-0.997415\pi$
$557$	−11.6340	+	20.1507i	−0.492949	+	0.853813i	0.507018	+	0.861936i	$0.330748\pi$
$558$		0			0
$559$	29.0993			1.23077
$560$		0			0
$561$	−33.0097	−	19.0582i	−1.39367	−	0.804637i
$562$		0			0
$563$	−14.1540			−0.596519			−0.298259	−	0.954485i	$-0.596406\pi$
$563$	−14.1540			−0.596519			−0.298259	+	0.954485i	$0.596406\pi$
$564$		0			0
$565$	−9.21422	+	5.31983i	−0.387645	+	0.223807i
$566$		0			0
$567$	4.88242	−	2.81886i	0.205042	−	0.118381i
$568$		0			0
$569$			39.8789i			1.67181i	0.548875	+	0.835904i	$0.315056\pi$
$569$			39.8789i			1.67181i	−0.548875	+	0.835904i	$0.684944\pi$
$570$		0			0
$571$		−	29.5709i		−	1.23750i	−0.785587	−	0.618752i	$-0.787639\pi$
$571$		−	29.5709i		−	1.23750i	0.785587	−	0.618752i	$-0.212361\pi$
$572$		0			0
$573$	−1.16039	+	0.669951i	−0.0484760	+	0.0279876i
$574$		0			0
$575$	3.18133	−	1.83674i	0.132671	−	0.0765974i
$576$		0			0
$577$	−5.56696			−0.231756			−0.115878	−	0.993263i	$-0.536968\pi$
$577$	−5.56696			−0.231756			−0.115878	+	0.993263i	$0.536968\pi$
$578$		0			0
$579$	−8.06214	−	4.65468i	−0.335051	−	0.193442i
$580$		0			0
$581$	−11.6811			−0.484614
$582$		0			0
$583$	−14.0514	+	24.3377i	−0.581948	+	1.00796i
$584$		0			0
$585$	8.65270	+	4.99564i	0.357745	+	0.206544i
$586$		0			0
$587$	35.3257	−	20.3953i	1.45805	−	0.841804i	0.459132	−	0.888368i	$-0.348161\pi$
$587$	35.3257	−	20.3953i	1.45805	−	0.841804i	0.998915	+	0.0465645i	$0.0148273\pi$
$588$		0			0
$589$	−43.5130	+	6.30954i	−1.79292	+	0.259980i
$590$		0			0
$591$	−8.65162	−	14.9850i	−0.355880	−	0.616402i
$592$		0			0
$593$	12.7625	−	22.1053i	0.524093	−	0.907756i	−0.475513	−	0.879709i	$-0.657738\pi$
$593$	12.7625	−	22.1053i	0.524093	−	0.907756i	0.999607	−	0.0280477i	$-0.00892903\pi$
$594$		0			0
$595$	10.2849	+	5.93799i	0.421640	+	0.243434i
$596$		0			0
$597$		−	11.9810i		−	0.490350i
$598$		0			0
$599$	−14.9833	+	25.9519i	−0.612203	+	1.06037i	0.378666	+	0.925534i	$0.376383\pi$
$599$	−14.9833	+	25.9519i	−0.612203	+	1.06037i	−0.990868	+	0.134833i	$0.956950\pi$
$600$		0			0
$601$		−	14.0213i		−	0.571941i	−0.958238	−	0.285971i	$-0.907684\pi$
$601$		−	14.0213i		−	0.571941i	0.958238	−	0.285971i	$-0.0923160\pi$
$602$		0			0
$603$	−4.22694	−	7.32127i	−0.172134	−	0.298145i
$604$		0			0
$605$	12.4439	+	21.5534i	0.505915	+	0.876271i
$606$		0			0
$607$	−41.1479			−1.67014			−0.835071	−	0.550143i	$-0.814573\pi$
$607$	−41.1479			−1.67014			−0.835071	+	0.550143i	$0.814573\pi$
$608$		0			0
$609$	4.69680			0.190324
$610$		0			0
$611$	15.8996	+	27.5388i	0.643227	+	1.11410i
$612$		0			0
$613$	−5.58019	−	9.66518i	−0.225382	−	0.390373i	0.731052	−	0.682322i	$-0.239030\pi$
$613$	−5.58019	−	9.66518i	−0.225382	−	0.390373i	−0.956434	+	0.291949i	$0.905696\pi$
$614$		0			0
$615$		−	0.500781i		−	0.0201935i
$616$		0			0
$617$	3.68137	−	6.37631i	0.148206	−	0.256701i	−0.782358	−	0.622829i	$-0.785983\pi$
$617$	3.68137	−	6.37631i	0.148206	−	0.256701i	0.930565	+	0.366128i	$0.119317\pi$
$618$		0			0
$619$			3.99121i			0.160420i	0.996778	+	0.0802102i	$0.0255592\pi$
$619$			3.99121i			0.160420i	−0.996778	+	0.0802102i	$0.974441\pi$
$620$		0			0
$621$	13.4197	+	7.74784i	0.538512	+	0.310910i
$622$		0			0
$623$	2.53159	−	4.38485i	0.101426	−	0.175675i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−16.0581	+	12.6594i	−0.641298	+	0.505569i
$628$		0			0
$629$	54.4118	−	31.4147i	2.16954	−	1.25259i
$630$		0			0
$631$	21.4372	+	12.3768i	0.853401	+	0.492711i	0.861797	−	0.507254i	$-0.169339\pi$
$631$	21.4372	+	12.3768i	0.853401	+	0.492711i	−0.00839609	+	0.999965i	$0.502673\pi$
$632$		0			0
$633$	−6.73844	+	11.6713i	−0.267829	+	0.463893i
$634$		0			0
$635$	−17.6199			−0.699224
$636$		0			0
$637$	−17.6320	−	10.1798i	−0.698604	−	0.403339i
$638$		0			0
$639$	−6.35077			−0.251232
$640$		0			0
$641$	−31.3856	+	18.1205i	−1.23966	+	0.715716i	−0.969024	−	0.246967i	$-0.920566\pi$
$641$	−31.3856	+	18.1205i	−1.23966	+	0.715716i	−0.270633	+	0.962683i	$0.587233\pi$
$642$		0			0
$643$	−19.0543	+	11.0010i	−0.751428	+	0.433837i	−0.826210	−	0.563363i	$-0.809507\pi$
$643$	−19.0543	+	11.0010i	−0.751428	+	0.433837i	0.0747816	+	0.997200i	$0.476174\pi$
$644$		0			0
$645$		−	5.44351i		−	0.214338i
$646$		0			0
$647$			27.4104i			1.07761i	0.842429	+	0.538807i	$0.181125\pi$
$647$			27.4104i			1.07761i	−0.842429	+	0.538807i	$0.818875\pi$
$648$		0			0
$649$	−16.3669	+	9.44945i	−0.642458	+	0.370923i
$650$		0			0
$651$	−9.99832	+	5.77253i	−0.391865	+	0.226243i
$652$		0			0
$653$	25.6900			1.00533			0.502664	−	0.864482i	$-0.332353\pi$
$653$	25.6900			1.00533			0.502664	+	0.864482i	$0.332353\pi$
$654$		0			0
$655$	−6.57870	−	3.79821i	−0.257051	−	0.148408i
$656$		0			0
$657$	8.70788			0.339727
$658$		0			0
$659$	−15.2303	+	26.3797i	−0.593289	+	1.02761i	0.400497	+	0.916298i	$0.368837\pi$
$659$	−15.2303	+	26.3797i	−0.593289	+	1.02761i	−0.993786	+	0.111308i	$0.964496\pi$
$660$		0			0
$661$	13.4286	+	7.75300i	0.522312	+	0.301557i	0.737880	−	0.674932i	$-0.235827\pi$
$661$	13.4286	+	7.75300i	0.522312	+	0.301557i	−0.215568	+	0.976489i	$0.569160\pi$
$662$		0			0
$663$	−23.0661	+	13.3172i	−0.895814	+	0.517199i
$664$		0			0
$665$	5.00324	−	3.94432i	0.194018	−	0.152954i
$666$		0			0
$667$	−7.53726	−	13.0549i	−0.291844	−	0.505489i
$668$		0			0
$669$	6.44941	−	11.1707i	0.249349	−	0.431885i
$670$		0			0
$671$	−43.9784	−	25.3910i	−1.69777	−	0.980207i
$672$		0			0
$673$		−	43.6943i		−	1.68429i	−0.539249	−	0.842146i	$-0.681292\pi$
$673$		−	43.6943i		−	1.68429i	0.539249	−	0.842146i	$-0.318708\pi$
$674$		0			0
$675$	2.10913	−	3.65312i	0.0811804	−	0.140609i
$676$		0			0
$677$			5.06169i			0.194537i	0.995258	+	0.0972683i	$0.0310105\pi$
$677$			5.06169i			0.194537i	−0.995258	+	0.0972683i	$0.968990\pi$
$678$		0			0
$679$	−0.0602574	−	0.104369i	−0.00231247	−	0.00400531i
$680$		0			0
$681$	−1.93398	−	3.34976i	−0.0741104	−	0.128363i
$682$		0			0
$683$	−48.7930			−1.86701			−0.933507	−	0.358559i	$-0.883268\pi$
$683$	−48.7930			−1.86701			−0.933507	+	0.358559i	$0.883268\pi$
$684$		0			0
$685$	13.0176			0.497376
$686$		0			0
$687$	−1.22110	−	2.11501i	−0.0465880	−	0.0806928i
$688$		0			0
$689$	9.81863	+	17.0064i	0.374060	+	0.647891i
$690$		0			0
$691$		−	11.3620i		−	0.432231i	−0.976368	−	0.216116i	$-0.930661\pi$
$691$		−	11.3620i		−	0.432231i	0.976368	−	0.216116i	$-0.0693388\pi$
$692$		0			0
$693$	10.4494	−	18.0989i	0.396940	−	0.687521i
$694$		0			0
$695$			6.45069i			0.244689i
$696$		0			0
$697$	−4.50000	−	2.59808i	−0.170450	−	0.0984092i
$698$		0			0
$699$	2.13752	−	3.70229i	0.0808483	−	0.140033i
$700$		0			0
$701$	7.03625	+	12.1871i	0.265756	+	0.460302i	0.967761	−	0.251869i	$-0.0810452\pi$
$701$	7.03625	+	12.1871i	0.265756	+	0.460302i	−0.702006	+	0.712171i	$0.747712\pi$
$702$		0			0
$703$	−4.83686	−	33.3568i	−0.182426	−	1.25808i
$704$		0			0
$705$	5.15160	−	2.97428i	0.194021	−	0.112018i
$706$		0			0
$707$	−17.2620	−	9.96623i	−0.649205	−	0.374819i
$708$		0			0
$709$	6.29227	−	10.8985i	0.236311	−	0.409303i	−0.723342	−	0.690490i	$-0.757395\pi$
$709$	6.29227	−	10.8985i	0.236311	−	0.409303i	0.959653	+	0.281187i	$0.0907282\pi$
$710$		0			0
$711$	−39.6972			−1.48876
$712$		0			0
$713$	32.0899	+	18.5271i	1.20178	+	0.693846i
$714$		0			0
$715$	25.0772			0.937834
$716$		0			0
$717$	6.72301	−	3.88153i	0.251075	−	0.144958i
$718$		0			0
$719$	−4.28700	+	2.47510i	−0.159878	+	0.0923056i	−0.577804	−	0.816175i	$-0.696090\pi$
$719$	−4.28700	+	2.47510i	−0.159878	+	0.0923056i	0.417926	+	0.908481i	$0.362757\pi$
$720$		0			0
$721$			13.5659i			0.505221i
$722$		0			0
$723$		−	20.1192i		−	0.748241i
$724$		0			0
$725$	−3.55383	+	2.05180i	−0.131986	+	0.0762021i
$726$		0			0
$727$	15.1641	−	8.75500i	0.562406	−	0.324705i	−0.191705	−	0.981453i	$-0.561402\pi$
$727$	15.1641	−	8.75500i	0.562406	−	0.324705i	0.754111	+	0.656747i	$0.228068\pi$
$728$		0			0
$729$	0.703287			0.0260477
$730$		0			0
$731$	−48.9152	−	28.2412i	−1.80919	−	1.04454i
$732$		0			0
$733$	39.1669			1.44666			0.723331	−	0.690502i	$-0.242610\pi$
$733$	39.1669			1.44666			0.723331	+	0.690502i	$0.242610\pi$
$734$		0			0
$735$	−1.90431	+	3.29836i	−0.0702414	+	0.121662i
$736$		0			0
$737$	−18.3757	−	10.6092i	−0.676878	−	0.390796i
$738$		0			0
$739$	−23.9097	+	13.8042i	−0.879531	+	0.507797i	−0.870504	−	0.492162i	$-0.836207\pi$
$739$	−23.9097	+	13.8042i	−0.879531	+	0.507797i	−0.00902716	+	0.999959i	$0.502873\pi$
$740$		0			0
$741$	2.05043	+	14.1406i	0.0753245	+	0.519466i
$742$		0			0
$743$	3.36804	+	5.83362i	0.123562	+	0.214015i	0.921170	−	0.389161i	$-0.127235\pi$
$743$	3.36804	+	5.83362i	0.123562	+	0.214015i	−0.797608	+	0.603176i	$0.793902\pi$
$744$		0			0
$745$	0.193398	−	0.334976i	0.00708556	−	0.0122726i
$746$		0			0
$747$	16.5195	+	9.53753i	0.604417	+	0.348960i
$748$		0			0
$749$		−	18.1441i		−	0.662972i
$750$		0			0
$751$	16.7275	−	28.9729i	0.610396	−	1.05724i	−0.380778	−	0.924667i	$-0.624344\pi$
$751$	16.7275	−	28.9729i	0.610396	−	1.05724i	0.991174	−	0.132570i	$-0.0423230\pi$
$752$		0			0
$753$			12.2789i			0.447469i
$754$		0			0
$755$	−3.22348	−	5.58323i	−0.117314	−	0.203195i
$756$		0			0
$757$	−6.75047	−	11.6922i	−0.245350	−	0.424959i	0.716880	−	0.697197i	$-0.245570\pi$
$757$	−6.75047	−	11.6922i	−0.245350	−	0.424959i	−0.962230	+	0.272238i	$0.912236\pi$
$758$		0			0
$759$	17.2327			0.625507
$760$		0			0
$761$	23.4482			0.849997			0.424999	−	0.905194i	$-0.360275\pi$
$761$	23.4482			0.849997			0.424999	+	0.905194i	$0.360275\pi$
$762$		0			0
$763$	−8.22066	−	14.2386i	−0.297608	−	0.515472i
$764$		0			0
$765$	−9.69664	−	16.7951i	−0.350583	−	0.607227i
$766$		0			0
$767$			13.2059i			0.476839i
$768$		0			0
$769$	−0.550585	+	0.953642i	−0.0198546	+	0.0343892i	−0.875782	−	0.482707i	$-0.839654\pi$
$769$	−0.550585	+	0.953642i	−0.0198546	+	0.0343892i	0.855927	+	0.517096i	$0.172987\pi$
$770$		0			0
$771$			11.0443i			0.397750i
$772$		0			0
$773$	−36.5449	−	21.0992i	−1.31443	−	0.758885i	−0.331602	−	0.943419i	$-0.607589\pi$
$773$	−36.5449	−	21.0992i	−1.31443	−	0.758885i	−0.982826	+	0.184534i	$0.940922\pi$
$774$		0			0
$775$	5.04348	−	8.73557i	0.181167	−	0.313791i
$776$		0			0
$777$	−4.42519	−	7.66466i	−0.158753	−	0.274968i
$778$		0			0
$779$	−2.18909	+	1.72578i	−0.0784324	+	0.0618324i
$780$		0			0
$781$	−13.8043	+	7.96992i	−0.493957	+	0.285186i
$782$		0			0
$783$	−14.9910	−	8.65504i	−0.535733	−	0.309306i
$784$		0			0
$785$	−0.621992	+	1.07732i	−0.0221998	+	0.0384512i
$786$		0			0
$787$	−2.42484			−0.0864363			−0.0432182	−	0.999066i	$-0.513761\pi$
$787$	−2.42484			−0.0864363			−0.0432182	+	0.999066i	$0.513761\pi$
$788$		0			0
$789$	12.1428	+	7.01066i	0.432296	+	0.249586i
$790$		0			0
$791$	15.5511			0.552934
$792$		0			0
$793$	−30.7307	+	17.7424i	−1.09128	+	0.630050i
$794$		0			0
$795$	3.18133	−	1.83674i	0.112830	−	0.0651425i
$796$		0			0
$797$			7.58691i			0.268742i	0.990931	+	0.134371i	$0.0429014\pi$
$797$			7.58691i			0.268742i	−0.990931	+	0.134371i	$0.957099\pi$
$798$		0			0
$799$		−	61.7228i		−	2.18359i
$800$		0			0
$801$	−7.16039	+	4.13405i	−0.253000	+	0.146070i
$802$		0			0
$803$	18.9278	−	10.9280i	0.667949	−	0.385640i
$804$		0			0
$805$	−5.36922			−0.189240
$806$		0			0
$807$	4.50304	+	2.59983i	0.158515	+	0.0915184i
$808$		0			0
$809$	−13.3516			−0.469419			−0.234709	−	0.972066i	$-0.575414\pi$
$809$	−13.3516			−0.469419			−0.234709	+	0.972066i	$0.575414\pi$
$810$		0			0
$811$	9.68420	−	16.7735i	0.340058	−	0.588998i	−0.644385	−	0.764701i	$-0.722886\pi$
$811$	9.68420	−	16.7735i	0.340058	−	0.588998i	0.984443	+	0.175703i	$0.0562198\pi$
$812$		0			0
$813$	−9.11519	−	5.26266i	−0.319684	−	0.184570i
$814$		0			0
$815$	4.57198	−	2.63963i	0.160149	−	0.0924623i
$816$		0			0
$817$	−23.7955	+	18.7593i	−0.832500	+	0.656304i
$818$		0			0
$819$	−7.30171	−	12.6469i	−0.255142	−	0.441920i
$820$		0			0
$821$	−1.13402	+	1.96419i	−0.0395777	+	0.0685507i	−0.885136	−	0.465333i	$-0.845935\pi$
$821$	−1.13402	+	1.96419i	−0.0395777	+	0.0685507i	0.845558	+	0.533884i	$0.179268\pi$
$822$		0			0
$823$	−4.44552	−	2.56662i	−0.154961	−	0.0894669i	0.420514	−	0.907286i	$-0.361850\pi$
$823$	−4.44552	−	2.56662i	−0.154961	−	0.0894669i	−0.575475	+	0.817819i	$0.695183\pi$
$824$		0			0
$825$		−	4.69111i		−	0.163323i
$826$		0			0
$827$	−13.8912	+	24.0603i	−0.483046	+	0.836660i	−0.999810	−	0.0194678i	$-0.993803\pi$
$827$	−13.8912	+	24.0603i	−0.483046	+	0.836660i	0.516765	+	0.856127i	$0.327136\pi$
$828$		0			0
$829$		−	39.2914i		−	1.36465i	−0.731051	−	0.682323i	$-0.760970\pi$
$829$		−	39.2914i		−	1.36465i	0.731051	−	0.682323i	$-0.239030\pi$
$830$		0			0
$831$	−5.78440	−	10.0189i	−0.200659	−	0.347551i
$832$		0			0
$833$	19.7593	+	34.2240i	0.684618	+	1.18579i
$834$		0			0
$835$	12.5343			0.433766
$836$		0			0
$837$	42.5494			1.47072
$838$		0			0
$839$	20.6344	+	35.7398i	0.712379	+	1.23388i	0.963962	+	0.266040i	$0.0857154\pi$
$839$	20.6344	+	35.7398i	0.712379	+	1.23388i	−0.251583	+	0.967836i	$0.580951\pi$
$840$		0			0
$841$	−6.08019	−	10.5312i	−0.209662	−	0.363145i
$842$		0			0
$843$		−	11.0036i		−	0.378982i
$844$		0			0
$845$	2.26156	−	3.91714i	0.0778000	−	0.134754i
$846$		0			0
$847$		−	36.3763i		−	1.24991i
$848$		0			0
$849$	−8.60766	−	4.96963i	−0.295414	−	0.170557i
$850$		0			0
$851$	−14.2028	+	24.6000i	−0.486866	+	0.843277i
$852$		0			0
$853$	9.05707	+	15.6873i	0.310108	+	0.537123i	0.978386	−	0.206789i	$-0.0663013\pi$
$853$	9.05707	+	15.6873i	0.310108	+	0.537123i	−0.668277	+	0.743912i	$0.732968\pi$
$854$		0			0
$855$	−10.2961	+	1.49297i	−0.352120	+	0.0510587i
$856$		0			0
$857$	45.2503	−	26.1253i	1.54572	−	0.892423i	0.547261	−	0.836962i	$-0.315671\pi$
$857$	45.2503	−	26.1253i	1.54572	−	0.892423i	0.998461	−	0.0554604i	$-0.0176627\pi$
$858$		0			0
$859$	−14.0025	−	8.08436i	−0.477760	−	0.275835i	0.241723	−	0.970345i	$-0.422288\pi$
$859$	−14.0025	−	8.08436i	−0.477760	−	0.275835i	−0.719483	+	0.694511i	$0.755621\pi$
$860$		0			0
$861$	−0.365975	+	0.633888i	−0.0124724	+	0.0216028i
$862$		0			0
$863$	31.0577			1.05722			0.528609	−	0.848866i	$-0.322714\pi$
$863$	31.0577			1.05722			0.528609	+	0.848866i	$0.322714\pi$
$864$		0			0
$865$	−7.42859	−	4.28890i	−0.252580	−	0.145827i
$866$		0			0
$867$	38.3858			1.30365
$868$		0			0
$869$	−86.2875	+	49.8181i	−2.92710	+	1.68996i
$870$		0			0
$871$	−12.8403	+	7.41338i	−0.435079	+	0.251193i
$872$		0			0
$873$			0.196799i			0.00666063i
$874$		0			0
$875$			1.46162i			0.0494117i
$876$		0			0
$877$	−3.78673	+	2.18627i	−0.127869	+	0.0738250i	−0.562570	−	0.826750i	$-0.690187\pi$
$877$	−3.78673	+	2.18627i	−0.127869	+	0.0738250i	0.434701	+	0.900575i	$0.356854\pi$
$878$		0			0
$879$	−10.7186	+	6.18838i	−0.361529	+	0.208729i
$880$		0			0
$881$	38.7866			1.30675			0.653376	−	0.757033i	$-0.273352\pi$
$881$	38.7866			1.30675			0.653376	+	0.757033i	$0.273352\pi$
$882$		0			0
$883$	−20.8450	−	12.0348i	−0.701489	−	0.405005i	0.106413	−	0.994322i	$-0.466064\pi$
$883$	−20.8450	−	12.0348i	−0.701489	−	0.405005i	−0.807902	+	0.589317i	$0.799397\pi$
$884$		0			0
$885$	2.47039			0.0830413
$886$		0			0
$887$	6.24054	−	10.8089i	0.209537	−	0.362928i	−0.742032	−	0.670365i	$-0.766138\pi$
$887$	6.24054	−	10.8089i	0.209537	−	0.362928i	0.951569	+	0.307436i	$0.0994711\pi$
$888$		0			0
$889$	22.3032	+	12.8768i	0.748025	+	0.431873i
$890$		0			0
$891$	−20.0113	+	11.5535i	−0.670402	+	0.387057i
$892$		0			0
$893$	−30.7549	−	12.2696i	−1.02917	−	0.410587i
$894$		0			0
$895$	−12.5695	−	21.7711i	−0.420153	−	0.727726i
$896$		0			0
$897$	6.02082	−	10.4284i	0.201029	−	0.348193i
$898$		0			0
$899$	−35.8474	−	20.6965i	−1.19558	−	0.690266i
$900$		0			0
$901$		−	38.1164i		−	1.26984i
$902$		0			0
$903$	−3.97816	+	6.89038i	−0.132385	+	0.229298i
$904$		0			0
$905$			11.0102i			0.365993i
$906$		0			0
$907$	4.91702	+	8.51653i	0.163267	+	0.282787i	0.936039	−	0.351898i	$-0.114463\pi$
$907$	4.91702	+	8.51653i	0.163267	+	0.282787i	−0.772771	+	0.634684i	$0.781130\pi$
$908$		0			0
$909$	16.2747	+	28.1886i	0.539798	+	0.934957i
$910$		0			0
$911$	17.9535			0.594826			0.297413	−	0.954749i	$-0.403876\pi$
$911$	17.9535			0.594826			0.297413	+	0.954749i	$0.403876\pi$
$912$		0			0
$913$	47.8767			1.58449
$914$		0			0
$915$	3.31901	+	5.74869i	0.109723	+	0.190046i
$916$		0			0
$917$	5.55153	+	9.61553i	0.183328	+	0.317533i
$918$		0			0
$919$		−	17.9851i		−	0.593274i	−0.954990	−	0.296637i	$-0.904135\pi$
$919$		−	17.9851i		−	0.593274i	0.954990	−	0.296637i	$-0.0958651\pi$
$920$		0			0
$921$	10.5154	−	18.2133i	0.346495	−	0.600147i
$922$		0			0
$923$			11.1382i			0.366620i
$924$		0			0
$925$	6.69664	+	3.86631i	0.220184	+	0.127123i
$926$		0			0
$927$	11.0765	−	19.1850i	0.363799	−	0.630118i
$928$		0			0
$929$	1.04948	+	1.81776i	0.0344325	+	0.0596388i	0.882728	−	0.469884i	$-0.155704\pi$
$929$	1.04948	+	1.81776i	0.0344325	+	0.0596388i	−0.848296	+	0.529523i	$0.822371\pi$
$930$		0			0
$931$	20.9809	−	3.04230i	0.687620	−	0.0997073i
$932$		0			0
$933$	−16.2241	+	9.36699i	−0.531153	+	0.306662i
$934$		0			0
$935$	−42.1541	−	24.3377i	−1.37859	−	0.795927i
$936$		0			0
$937$	−21.6396	+	37.4808i	−0.706934	+	1.22445i	0.259055	+	0.965863i	$0.416589\pi$
$937$	−21.6396	+	37.4808i	−0.706934	+	1.22445i	−0.965989	+	0.258583i	$0.916744\pi$
$938$		0			0
$939$	−4.45060			−0.145240
$940$		0			0
$941$	−32.3208	−	18.6604i	−1.05363	−	0.608312i	−0.129965	−	0.991519i	$-0.541486\pi$
$941$	−32.3208	−	18.6604i	−1.05363	−	0.608312i	−0.923663	+	0.383207i	$0.874820\pi$
$942$		0			0
$943$	2.34922			0.0765011
$944$		0			0
$945$	−5.33946	+	3.08274i	−0.173693	+	0.100281i
$946$		0			0
$947$	−24.5816	+	14.1922i	−0.798796	+	0.461185i	−0.843050	−	0.537835i	$-0.819242\pi$
$947$	−24.5816	+	14.1922i	−0.798796	+	0.461185i	0.0442541	+	0.999020i	$0.485909\pi$
$948$		0			0
$949$		−	15.2722i		−	0.495758i
$950$		0			0
$951$			17.9481i			0.582006i
$952$		0			0
$953$	−39.6273	+	22.8788i	−1.28365	+	0.741118i	−0.977514	−	0.210869i	$-0.932371\pi$
$953$	−39.6273	+	22.8788i	−1.28365	+	0.741118i	−0.306139	+	0.951987i	$0.599037\pi$
$954$		0			0
$955$	−1.48184	+	0.855541i	−0.0479512	+	0.0276847i
$956$		0			0
$957$	−19.2505			−0.622279
$958$		0			0
$959$	−16.4776	−	9.51335i	−0.532090	−	0.307202i
$960$		0			0
$961$	70.7468			2.28216
$962$		0			0
$963$	−14.8145	+	25.6595i	−0.477392	+	0.826867i
$964$		0			0
$965$	−10.2955	−	5.94412i	−0.331424	−	0.191348i
$966$		0			0
$967$	17.7885	−	10.2702i	0.572040	−	0.330267i	−0.185924	−	0.982564i	$-0.559528\pi$
$967$	17.7885	−	10.2702i	0.572040	−	0.330267i	0.757964	+	0.652297i	$0.226194\pi$
$968$		0			0
$969$	10.2768	−	25.7599i	0.330140	−	0.827526i
$970$		0			0
$971$	4.20289	+	7.27962i	0.134877	+	0.233614i	0.925551	−	0.378624i	$-0.123603\pi$
$971$	4.20289	+	7.27962i	0.134877	+	0.233614i	−0.790673	+	0.612238i	$0.790269\pi$
$972$		0			0
$973$	4.71422	−	8.16527i	0.151131	−	0.261766i
$974$		0			0
$975$	−2.83883	−	1.63900i	−0.0909152	−	0.0524899i
$976$		0			0
$977$			3.49691i			0.111876i	0.998434	+	0.0559380i	$0.0178149\pi$
$977$			3.49691i			0.111876i	−0.998434	+	0.0559380i	$0.982185\pi$
$978$		0			0
$979$	−10.3761	+	17.9719i	−0.331621	+	0.574385i
$980$		0			0
$981$			26.8484i			0.857204i
$982$		0			0
$983$	15.2260	+	26.3722i	0.485633	+	0.841141i	0.999864	−	0.0165107i	$-0.00525577\pi$
$983$	15.2260	+	26.3722i	0.485633	+	0.841141i	−0.514231	+	0.857652i	$0.671922\pi$
$984$		0			0
$985$	−11.0483	−	19.1362i	−0.352028	−	0.609730i
$986$		0			0
$987$	−8.69451			−0.276749
$988$		0			0
$989$	25.5361			0.812001
$990$		0			0
$991$	−13.2330	−	22.9203i	−0.420361	−	0.728086i	0.575614	−	0.817722i	$-0.304763\pi$
$991$	−13.2330	−	22.9203i	−0.420361	−	0.728086i	−0.995975	+	0.0896355i	$0.971430\pi$
$992$		0			0
$993$	−7.28903	−	12.6250i	−0.231310	−	0.400641i
$994$		0			0
$995$		−	15.3000i		−	0.485042i
$996$		0			0
$997$	25.8581	−	44.7876i	0.818935	−	1.41844i	−0.0875321	−	0.996162i	$-0.527898\pi$
$997$	25.8581	−	44.7876i	0.818935	−	1.41844i	0.906467	−	0.422276i	$-0.138769\pi$
$998$		0			0
$999$			32.6182i			1.03199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1520.2.bq.q.31.2	✓	12
4.3	odd	2	inner	1520.2.bq.q.31.5	yes	12
19.8	odd	6	inner	1520.2.bq.q.1471.5	yes	12
76.27	even	6	inner	1520.2.bq.q.1471.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1520.2.bq.q.31.2	✓	12	1.1	even	1	trivial
1520.2.bq.q.31.5	yes	12	4.3	odd	2	inner
1520.2.bq.q.1471.2	yes	12	76.27	even	6	inner
1520.2.bq.q.1471.5	yes	12	19.8	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1520.bq (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.391537 - 0.678161i) q^{3} +(-0.500000 - 0.866025i) q^{5} +1.46162i q^{7} +(1.19340 - 2.06703i) q^{9} +O(q^{10})\)	\(q+(-0.391537 - 0.678161i) q^{3} +(-0.500000 - 0.866025i) q^{5} +1.46162i q^{7} +(1.19340 - 2.06703i) q^{9} -5.99064i q^{11} +(-3.62524 - 2.09303i) q^{13} +(-0.391537 + 0.678161i) q^{15} +(4.06262 + 7.03666i) q^{17} +(4.31378 - 0.625514i) q^{19} +(0.991212 - 0.572276i) q^{21} +(-3.18133 - 1.83674i) q^{23} +(-0.500000 + 0.866025i) q^{25} -4.21826 q^{27} +(3.55383 + 2.05180i) q^{29} -10.0870 q^{31} +(-4.06262 + 2.34555i) q^{33} +(1.26580 - 0.730808i) q^{35} -7.73262i q^{37} +3.27799i q^{39} +(-0.553830 + 0.319754i) q^{41} +(-6.02015 + 3.47574i) q^{43} -2.38680 q^{45} +(-6.57870 - 3.79821i) q^{47} +4.86368 q^{49} +(3.18133 - 5.51022i) q^{51} +(-4.06262 - 2.34555i) q^{53} +(-5.18804 + 2.99532i) q^{55} +(-2.11320 - 2.68053i) q^{57} +(-1.57737 - 2.73208i) q^{59} +(4.23844 - 7.34119i) q^{61} +(3.02120 + 1.74429i) q^{63} +4.18606i q^{65} +(1.77097 - 3.06740i) q^{67} +2.87660i q^{69} +(-1.33040 - 2.30431i) q^{71} +(1.82418 + 3.15957i) q^{73} +0.783073 q^{75} +8.75602 q^{77} +(-8.31600 - 14.4037i) q^{79} +(-1.92859 - 3.34042i) q^{81} +7.99191i q^{83} +(4.06262 - 7.03666i) q^{85} -3.21343i q^{87} +(-3.00000 - 1.73205i) q^{89} +(3.05921 - 5.29871i) q^{91} +(3.94941 + 6.84059i) q^{93} +(-2.69860 - 3.42309i) q^{95} +(-0.0714065 + 0.0412266i) q^{97} +(-12.3828 - 7.14922i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{5} - 4 q^{9}+O(q^{10}) \) 12 * q - 6 * q^5 - 4 * q^9	\( 12 q - 6 q^{5} - 4 q^{9} + 18 q^{13} + 18 q^{17} + 24 q^{21} - 6 q^{25} + 24 q^{29} - 18 q^{33} + 12 q^{41} + 8 q^{45} - 28 q^{49} - 18 q^{53} - 62 q^{57} + 26 q^{61} + 16 q^{73} + 56 q^{77} - 66 q^{81} + 18 q^{85} - 36 q^{89} - 20 q^{93} + 42 q^{97}+O(q^{100}) \) 12 * q - 6 * q^5 - 4 * q^9 + 18 * q^13 + 18 * q^17 + 24 * q^21 - 6 * q^25 + 24 * q^29 - 18 * q^33 + 12 * q^41 + 8 * q^45 - 28 * q^49 - 18 * q^53 - 62 * q^57 + 26 * q^61 + 16 * q^73 + 56 * q^77 - 66 * q^81 + 18 * q^85 - 36 * q^89 - 20 * q^93 + 42 * q^97

Introduction

L-functions

Modular forms

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Database

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